Method for prediction of key performance parameter of an aero-engine transition state acceleration process based on space reconstruction

ABSTRACT

A method for prediction of key performance parameters of an aero-engine transition state acceleration process based on space reconstruction. Aero-engine transition state acceleration process test data provided by a research institute is used for establishing a training dataset and a testing dataset; dimension increase is conducted on the datasets based on the data space reconstruction of an auto-encoder; model parameters optimization is conducted by population optimization algorithms which is represented by particle swarm algorithm; and random forest regression algorithm performing well on high-dimensional data is used for carrying out regression on transition state performance parameters, which realizes effective real-time prediction from the perspective of engineering application.

TECHNICAL FIELD

The present invention belongs to the technical field of aero-engineperformance parameter prediction and particularly relates to a methodfor prediction of key performance parameter of an aero-engine transitionstate acceleration process based on space reconstruction.

BACKGROUND

The possibility of failure of an aero-engine operating in a complexenvironment with high temperature, high pressure and high speed for along time increases over time. The performance of the transition stateacceleration process directly relates to the progress of the takeoff andaccelerated flight process of an aircraft. Since the mechanism of anaero-engine is extremely complex, it is difficult to model thetransition state process parameters. Therefore, the data driven-basedaero-engine performance parameter advanced prediction method can avoidbuilding the model of the engine mechanism with complex process, andprovide early forecast for the parameter state of the engine transitionstate acceleration process to ensure the safety of life and property.

Many domestic and foreign scholars have done relevant work on datadriven-based aero-engine transient state performance parameterprediction. However, the traditional prediction algorithm has highrequirements for model parameters and input features, and usually has toadjust the parameters by the optimization algorithm before modeling; allparameter features of different types of engines have different degreesof influence on model prediction accuracy, and features are needed to bere-selected; the change rule of the transition state accelerationprocess parameters is complex, and the degree of influence of the modelparameters on the prediction accuracy is large; the traditionalregression prediction algorithm performs poorly on the high-dimensionaldata sample, and the spatial dimension of the transient stateacceleration process data sample is far from enough to describe theaero-engine performance; and the generalization ability of the model ispoor, so when the engine is changed, there is a need to re-select themodel parameters and input features, which increases the human andfinancial consumption to a certain extent.

Therefore, aiming at difficulties in model parameters selection, thepresent invention proposes a parameter prediction method based on aRandom Forest (RF) algorithm. Compared with the traditional machinelearning regression algorithm, the RF algorithm has the advantages ofinsensitivity to multivariate collinearity, high prediction accuracy,high convergence rate, less and easy-to-understand adjustableparameters, good performance on high-dimensional data, no over fitting,etc. With the characteristics of high efficiency and accuracy, RandomForest is increasingly used in all walks of life. Aiming at difficultiesin feature selection, the present invention proposes a neuralnetwork-based sparse auto-encoder (SAE) for conducting dimensionincrease and reduction on input features. Compared with the traditionalfeature selection algorithms (such as PCA), the dimension increase andreduction of the features by SAE can be adjusted according to thealgorithm, which has the effect of improving the prediction accuracy foralgorithms such as RF algorithm which show accurate prediction effecteven on independent variables with high dimension. For the twoalgorithms, the parameter optimization algorithm is adopted to optimizethe model parameters, and from the perspective of practical engineeringapplication, the key performance parameters of the engine, such ascompressor physical speed and exhaust gas temperature, are predicted.

SUMMARY

Aiming at the above-mentioned defects existing in the prior art, thepresent invention provides a method for prediction of performanceparameters of an aero-engine transition state acceleration process basedon space reconstruction.

The technical solution of the present invention is:

A method for prediction of key performance parameters of an aero-enginetransition state acceleration process based on space reconstruction,comprising the following steps:

Step 1: preprocessing aero-engine test data;

(1) Aero-engine transition state acceleration process test datacomprises 10 kinds of parameters: compressor inlet relative speedPNNC2_(g), engine inlet temperature T₂, engine inlet pressure P₂,compressor outlet total pressure P₃, fuel flow WFB, fan physical speedN_(f), compressor physical speed N_(c), exhaust gas temperature T₅,simulated altitude H and simulated Mach Ma, which are considered as onesample;

(2) Data storage and reading: the aero-engine transition stateacceleration process test data comprises data collected at multipleaero-engine commissioning process sites. Combining the data collected atmultiple aero-engine commissioning process sites for the aero-engineacceleration process, and storing the data uniformly, then establishingan aero-engine performance parameter test database;

(3) Linear resampling: analyzing aero-engine acceleration process testdata. Because sampling time intervals are different, a linear resamplingmethod is adopted to resample the aero-engine acceleration process testdata to make the sampling frequencies of signal identical;

(4) Data screening and cleaning: conducting visualization processing onthe linearly resampled aero-engine transition state acceleration processtest data, and conducting cleaning on acceleration curves whichobviously do not meet objective conditions;

Step 2: conducting Random Forest regression model parameters selection;

The Random Forest regression model has two key parameters: ntree whichis the number of Regression Trees in the Random Forest regression model,if ntree is too small, the accuracy of the model prediction is low, andif ntree is too large, the calculation time that is too long isdisadvantageous to real-time prediction; and mtry which is the featurenumber of Regression Trees in the Random Forest regression model, i.e.the number of branches of each Regression Tree; because the parameter ofthe Random Forest regression model is a dispersed integer value,two-dimensional grid search is selected for ergodic calculation of theparameters ntree and mtry, and MSE is selected for a fitness function(i.e. the returned value of parameter optimization); and theoptimization range of the two-dimensional grid search is determined bythe following principles:

(1) the optimization range of ntree is determined by the out-of-bagerror rate (OOB error rate), wherein the OOB error rate is the errorrate caused by the regression of the data which is not selected as thetraining sample for a single Decision Tree at a time; variation curvesof OOB calculated for compressor physical speed N_(c) and engine exhaustgas temperature EGT as the predicted test data feature parameters aswell as the parameter ntree are shown in FIG. 2; and therefore theoptimization range of ntree is determined to be 50˜500;

(2) the optimization range of mtry is determined to be from the naturalnumber 1 to the total feature number of the test data;

The Random Forest regression model parameters selection of the presentinvention is determined to be ntree=300 and mtry=D/3 by the gridoptimization algorithm, wherein D is the number of input variables ofthe model;

Step 3: establishing a training database by using a sparse auto-encoder;

After determining the parameters of the Random Forest regression model,determining the related parameters of SAE by using an SAE-RF hybridmodel. Because it is difficult for 10 parameter features of theaero-engine test data to meet the accuracy requirement of theaero-engine transition state parameter prediction model, the sparserepresentation of the aero-engine test data is selected to be learnedout to mine more information from 10-dimensional input variable.Establishing the input vector of the model by using SAE with thestructure of 10-dim-10. In the present invention, the parameters of SAEare optimized by the dispersed-continuous hybrid particle swarmalgorithm (PSO), wherein the important parameters of SAE compriselearning rate α and reconstructed dimension dim.

In the present invention, the principle of using the particle swarmalgorithm for optimization is as follows: in two-dimensional parametersearching space, there is a population X=(X₁, X₂, . . . , X_(n))composed of n parameter combinations, wherein the position of the k^(th)parameter combination in the parameter searching space is expressed as atwo-dimensional vector X_(k)=(x_(k1), x_(k2)). Assuming the k^(th)parameter combination has the velocity V_(k)=(V_(k1), V_(k2))^(T) in thesearching space, the local best parameter thereof is P_(k)=(P_(k1),P_(k2))^(T) and the global best parameter of the parameter combinationis P_(g)=(P_(g1), P_(g2))^(T). In each iteration, the iterative formulasof the velocity and the position of the parameter combination areexpressed as:V _(k) ^(t+1) =wV _(k) ^(t) +c ₁ r ₁(P _(k) ^(t) −X _(k) ^(t))+c ₂ r ₂(P_(g) ^(t) −X _(k) ^(t))X _(k) ^(t+1) =X _(k) ^(t)+_(k) ^(t+1)where, w is inertia weight, t is the current number of iterations, r₁,r₂ are random numbers with uniform distribution in [0,1], and c₁, c₂ arelearning factor constants.

The K-fold cross-validation method is generally used for the estimationof generalization ability in parameters selection, and the specificsteps of optimizing the SAE-RF hybrid model parameters based on thedispersed-continuous hybrid particle swarm algorithm are as follows:

(1) randomly producing a group of {α, dim} as the initial position ofparticles, and determining inertia weight and learning factor;

(2) evenly splitting the training sample into k mutually exclusivesubsets S₁, S₂, . . . , S_(k);

(3) taking the value of the initial position of the population as aparameter to train the SAE-RF hybrid model, and calculating the averagevalue of k accuracies, which is the accuracy of the K-foldcross-validation;

(4) taking the accuracy of the K-fold cross-validation as the fitness ofthe particle swarm algorithm, calculating the local best position andthe global best position of the population, and iterating and updatingthe position and velocity;

(5) repeating the step (2) until the fitness requirements are met or themaximum number of iterations is reached;

(6) completing the parameter optimization, and taking the result as theparameter of the final SAE-RF hybrid model;

Step 4: building an SAE-RF regression model, predicting the aero-enginetest data, and evaluating the prediction effect.

Since the magnitude difference between the features after sparserepresentation of the aero-engine test data is large, the data sample isnormalized by a maximum value method to avoid the model error caused bythe magnitude difference. In the present invention, the features of theaero-engine transition state acceleration process test data after sparserepresentation are normalized into the interval [1,2] according to thefollowing formula:

$x_{k} = {\frac{x_{k} - x_{\min}}{x_{\max} - x_{\min}} + 1}$

Conducting regression prediction on the compressor physical speed N_(c)and engine exhaust gas temperature EGT by using the aero-enginetransition state acceleration process test data after dimensionreconstruction, and calculating the response evaluating indicator;

The main evaluating indicators comprise:

(1) relative error (RE)

The formula of the relative error is:

${{RE} = \frac{{\hat{y_{i}} - y_{i}}}{y_{i}}},{i = 1},{2\mspace{14mu}\ldots\mspace{14mu} N}$

where, ŷ_(ι) is the predicted value of the sample at the i^(th) moment,y_(i) is the observed value of the sample at the i^(th) moment, and N isthe length of the sample;

(2) mean square error (MSE)

The mean square error is a measure reflecting the difference between thepredicted sequence and the observed sequence, and is calculatedaccording to the following formula:

${MSE} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}( {y_{i} - \hat{y_{i}}} )^{2}}}$where, ŷ_(ι) is the predicted value of the sample at the i^(th) moment,y_(i) is the observed value of the sample at the i^(th) moment, and N isthe length of the sample.

The present invention has the following beneficial effects that: in thepresent invention, aero-engine transition state acceleration processtest data provided by a research institute is used for establishing atraining dataset and a testing dataset; dimension increase is conductedon the datasets based on the data space reconstruction of anauto-encoder; population optimization algorithms represented by aparticle swarm algorithm (PSO) are adopted to optimize model parameters;and finally, a Random Forest regression algorithm performing well onhigh-dimensional data is used for regressing transition stateperformance parameters, which realizes effective real-time predictionfrom the perspective of engineering application.

DESCRIPTION OF DRAWINGS

FIG. 1 is a flow chart of establishing an aero-engine transition stateacceleration process key performance parameter prediction model.

FIG. 2 is a curve graph showing a relationship between the out-of-bagerror rate and the number of Decision Trees of the model.

FIG. 3 is a diagram of a best parameter result of a Random Forestregression model for grid search.

FIG. 4 is a curve graph showing a parameter optimization process of aparticle swarm algorithm, wherein the upper part is a diagram of theoptimized result of the particle swarm algorithm predicting compressorphysical speed, and the lower part is a diagram of the optimized resultof the particle swarm algorithm predicting exhaust gas temperature.

FIG. 5 shows predicted curves and observed curves of 10 groups ofsamples, wherein the upper part is a diagram of predicted results ofcompressor physical speed, and the lower part is a diagram of predictedresults of exhaust gas temperature.

FIG. 6 is a schematic diagram of degree of deviation of predicted valuesfrom observed values of 10 groups of samples, wherein the upper part isa schematic diagram of degree of deviation of predicted values ofcompressor physical speed, and the lower part is a schematic diagram ofdegree of deviation of predicted values of exhaust gas temperature.

FIG. 7 is a distribution diagram of relative errors of 10 groups ofsamples, wherein the upper part is a distribution diagram of relativeerrors of compressor physical speed prediction, and the lower part is adistribution diagram of relative errors of exhaust gas temperatureprediction.

FIG. 8 is a distribution diagram of mean square errors of predictedsequence and observed sequence of 10 groups of samples, wherein theupper part is a diagram of mean square errors of compressor physicalspeed prediction, and the lower part is a diagram of mean square errorsof exhaust gas temperature prediction.

DETAILED DESCRIPTION

Specific embodiment of the present invention is further described belowin combination with accompanying drawings and the technical solution.

The data used in the present invention is 100 groups of transition stateacceleration process bench test data of a certain type of aero-engine,which are provided by a domestic research institute.

Step 1: preprocessing aero-engine test data;

(1) Aero-engine test data comprises 10 groups of parameters: compressorinlet relative speed PNNC2_(g), engine inlet temperature T₂, engineinlet pressure P₂, compressor outlet total pressure P₃, fuel flow WFB,fan physical speed N_(f), compressor physical speed N_(c), exhaust gastemperature T₅, simulated altitude H and simulated Mach Ma;

(2) Data integration: reading, integrating and storing txt files of 100groups of data, and establishing an aero-engine test database.

(3) Resampling: resampling the data first due to different samplingintervals. The specific steps are as follows: inserting the proposed newsampling frequency as an interpolation into the time series of theoriginal data by using an interpolation method, and counting the numberof original data between nominal sampling points. If only one originaldata is included, taking the original data as the data corresponding tothe sampling point; if two original data are included, calculating theaverage value of the two original data, and taking the average value asthe data corresponding to the time point; and if no original data isincluded, taking the average value of the data corresponding to theprevious time point and the next time point of the time point in thenominal time series as the data of the time point.

(4) Data screening and cleaning: conducting visualization processing onthe data in order to conduct simple clustering and cleaning onacceleration curves.

Step 2: conducting Random Forest regression model parameters selection;

In the present invention, the parameter optimization range based on gridresearch is determined according to FIG. 2, finally the optimizationrange of 50 to 500 and the optimization step length of 10 for ntree areselected; selecting the optimization range of 1 to D and theoptimization step length of 1 for mtry, wherein D is the dimension ofthe input vector of the model, i.e. the dimension of the test datasamples. Calculating the value of the fitness function by the 3-foldcross-validation method, splitting 90 groups of test data samples intothree parts, and conducting three prediction tasks on each part.m _(k) =saerftrain(x ^(tr) ^(k) ,y ^(tr) ^(k) ,ntree,mtry)k=1,2,3

Taking the average value of mean square errors of the three tasks as thevalue of the fitness function corresponding to this group of parameters:

${mse}_{k} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}( {{{saerfregression}( {x^{{te}_{k}},m_{k},{ntree},{mtry}} )} - y^{{te}_{k}}} )^{2}}}$k = 1, 2, 3 MSE = (mse₁ + mse₂ + mse₃)/3

The final optimization result is shown in FIG. 3. Considering theinfluence factors such as time cost and calculated amount, the finalparameter selection results are ntree=300, mtry=D/3, wherein D is thedimension of the input vector of the model.

Step 3: establishing a training database by using a sparse auto-encoder;

The important parameters of the sparse auto-encoder in the presentinvention comprise learning rate α and reconstructed dimension dim,wherein α is a continuous value and dim is a dispersed integer value, soa dispersed-continuous hybrid particle swarm algorithm is used foroptimization in two dimensions of parameters, and the 3-foldcross-validation method is also used. Setting the number of groups inthe initial population to 10 and the maximum number of iterations to 50,and randomly setting the initial position of particles to {[0,1],{1,2 .. . 50}}. Attention is needed to limit dim to not lower than 1 or largerthan 50 during random setting of the initial velocity of particles.Setting the inertia weight to

$\frac{1}{2\;\ln\; 2}$and the learning factor to c₁=c₂=0.5+ln2.

The parameter optimization result of SAE is shown in FIG. 4. The localbest solution at the number of iterations when the minimum value of thefitness function is reached is selected as the parameter result: settingthe parameters to dim=46, α=0.7060 during compressor physical speedprediction; and setting the parameters to dim=20, α=1.7428 duringexhaust gas temperature prediction.

Step 4: building an SAE-RF regression model, predicting the aero-enginetest data, and evaluating the prediction effect.

Considering the large magnitude difference of the reconstructedaero-engine test data, conducting normalization processing by themaximum value method to increase the convergence rate and avoidreduction in the prediction accuracy caused by the magnitude difference.Normalizing the features of the test data after sparse representationinto the interval [1,2] according to the following formula:

$x_{k} = {\frac{x_{k} - x_{\min}}{x_{\max} - x_{\min}} + 1}$

Among 100 groups of test data provided by a domestic research instituteand used in the present invention, taking 90 groups as training data andthe remaining 10 groups as predicted data to respectively completeprediction tasks for compressor physical speed and exhaust gastemperature in the transition state acceleration process key parameters,calculating the relative error distribution and mean square error of 10groups of test data, and evaluating the prediction effect of the model.

As shown in FIG. 5 and FIG. 6, curves of the predicted values of themodel and the observed values of the test of compressor physical speednearly coincide, and the predicted values have almost no deviation fromthe observed values; and for the curves of the predicted values of themodel and the observed values of the test of exhaust gas temperature,the effect is slightly poorer than the prediction effect of thecompressor physical speed, and the predicted values have a large degreeof deviation from the observed values at the start of the sample test.The reason is that the measurable test data features are closely relatedto the compressor physical speed, but the thermal part of theaero-engine gas path has complex structure, the thermodynamicrelationship is difficult to describe, and the operating conditions ofthe sensor are harsh. FIG. 7 shows the distribution of relative errorsat each observation time point of 10 groups of predicted samples. Asshown in FIG. 8, even if the prediction effect of exhaust gastemperature is slightly poorer than that of compressor physical speed,the mean square errors of the 10 groups of predicted data samples can becompletely controlled below the requirement of aero-engine keyperformance parameter prediction software.

TABLE 1 Mean Square Errors of Predicted Samples Mean square error Meansquare error Sample of compressor of exhaust gas number physical speedtemperature 91 4.4756 × 10⁻⁵ 1.5095 × 10⁻² 92 6.2384 × 10⁻⁵ 1.2713 ×10⁻² 93 7.0633 × 10⁻⁵ 2.6651 × 10⁻² 94 1.3170 × 10⁻⁴ 2.4940 × 10⁻² 959.3826 × 10⁻⁵ 1.9236 × 10⁻² 96 1.2296 × 10⁻⁴ 1.6477 × 10⁻² 97 7.8499 ×10⁻⁵ 2.8127 × 10⁻² 98 7.9962 × 10⁻⁵ 2.3424 × 10⁻² 99 7.8157 × 10⁻⁵1.2246 × 10⁻² 100  8.3156 × 10⁻⁵ 1.8875 × 10⁻²

In conclusion, after the sparse auto-encoder based on the particle swarmalgorithm optimization conducting dimension reconstruction on theaero-engine transition state acceleration process test data, theaccuracy of predicting the key parameters such as compressor physicalspeed and exhaust gas temperature by the Random Forest regressionalgorithm can reach the desired effect. Therefore the present inventioncan be used in the fields of state prediction and fault diagnosis of anaero-engine.

The invention claimed is:
 1. A method for prediction of key performanceparameters of an aero-engine transition state acceleration process basedon space reconstruction, comprising the following steps: step 1:preprocessing aero-engine test data (1) aero-engine transition stateacceleration process test data comprises 10 kinds of parameters:compressor inlet relative speed PNNC2_(g), engine inlet temperature T₂,engine inlet pressure P₂, compressor outlet total pressure P₃, fuel flowWFB, fan physical speed N_(f), compressor physical speed N_(c), exhaustgas temperature T₅, simulated altitude H and simulated Mach Ma, whichare taken as one sample; (2) data storage and reading: the aero-enginetransition state acceleration process test data comprises data collectedat multiple aero-engine commissioning process sites; combining the datacollected at multiple aero-engine commissioning process sites for theaero-engine acceleration process and storing the collected datauniformly, then establishing an aero-engine performance parameter testdatabase; (3) linear resampling: analyzing aero-engine transition stateacceleration process test data; sampling different time intervals, alinear resampling method is adopted to resample the aero-enginetransition state acceleration process test data to make samplingfrequencies of signal identical; (4) data screening and cleaning:conducting visualization processing on the linearly resampledaero-engine transition state acceleration process test data, andconducting cleaning on acceleration curves which obviously do not meetobjective conditions; step 2: conducting Random Forest regression modelparameters selection the Random Forest regression model has two keyparameters: ntree which is the number of Regression Trees in the RandomForest regression model; and mtry which is the feature number ofRegression Trees in the Random Forest regression model, includes thenumber of branches of each Regression Tree; two-dimensional grid searchis selected for ergodic calculation of the parameters ntree and mtry,and Mean Square Error (MSE) is selected for a fitness function; and anoptimization range of the two-dimensional grid search is determined bythe following principles: (1) the optimization range of ntree isdetermined by the out-of-bag (OOB) error rate, wherein the out-of-bagerror rate is an error rate caused by the Forest regression model ofdata which is not selected as training sample for a single Decision Treeat a time; variation curves of OOB calculated for compressor physicalspeed N_(c) and engine exhaust gas temperature EGT as predicted testdata feature parameters as well as the parameter ntree are obtained; andtherefore the optimization range of ntree is determined to be 50˜500;(2) the optimization range of mtry is determined to be from the naturalnumber 1 to the total feature number of the test data; the Random Forestregression model parameters selection is finally determined to bentree=300 and mtry=D/3 by the grid optimization algorithm, wherein D isthe number of input variables of the Random Forest regression model;step 3: establishing a training database by using a sparse auto-encoderafter determining the parameters of the Random Forest regression model,determining related parameters of Sparse Auto-Encoder (SAE) by using anSparse Auto-Encoder Random Forest (SAE-RF) hybrid model; establishing aninput vector of the SAE-RF hybrid model by using SAE with the structureof 10-dim-10; and optimizing the parameters of SAE by adispersed-continuous hybrid particle swarm algorithm, wherein parametersof SAE comprise learning rate a and reconstructed dimension dim; usingthe particle swarm algorithm for optimization as follows: intwo-dimensional parameter searching space, there is a population X=(X₁,X₂, . . . , X_(n)) composed of n parameter combinations, wherein theposition of the k^(th) parameter combination in the parameter searchingspace is expressed as a two-dimensional vector X_(k)=(x_(k1),x_(k2));assuming the k^(th) parameter combination has the velocityV_(k)=(V_(k1),V_(k2))^(T) in the parameter searching space, the localbest parameter thereof is P_(k)=(P_(k1),P_(k2))^(T), and the global bestparameter of the parameter combination is P_(g)=(P_(g1),P_(g2))^(T); andin each iteration, the iterative formulas of the velocity and theposition of the parameter combination are expressed as:V _(k) ^(t+1) =wV _(k) ^(t) +c ₁ r ₁(P _(k) ^(t) −X _(k) ^(t))+c ₂ r ₂(P_(g) ^(t) −X _(k) ^(t))X _(k) ^(t+1) =X _(k) ^(t)+_(k) ^(t+1) where, w is inertia weight, t isthe current number of iterations, r₁,r₂ are random numbers with uniformdistribution in [0,1], and c₁,c₂ are learning factor constants; a K-foldcross-validation method is used for the estimation of generalizationability in parameters selection, and the specific steps of optimizingthe SAE-RF hybrid model parameters based on the dispersed-continuoushybrid particle swarm algorithm are as follows: (1) randomly producing agroup of {α, dim} as the initial position of particles, and determininginertia weight and learning factor; (2) evenly splitting a trainingsample into k mutually exclusive subsets S₁, S₂, . . . , S_(k); (3)taking the value of the initial position of the population as aparameter to train the SAE-RF hybrid model, and calculating the averagevalue of k accuracies, which is the accuracy of the K-foldcross-validation; (4) taking the accuracy of the K-fold cross-validationas the fitness of the particle swarm algorithm, calculating the localbest position and the global best position of the population, anditerating and updating the position and velocity; (5) repeating the step(2) until the fitness requirements are met or the maximum number ofiterations is reached; (6) completing the parameter optimization, andtaking the result as the parameter of the final SAE-RF hybrid model;step 4: building an SAE-RF regression model, predicting the aero-enginetest data, and evaluating the prediction effect normalizing the datasample by a maximum value method to avoid the SAE-RF model error causedby magnitude difference; and normalizing the features of the aero-enginetransition state acceleration process test data after sparserepresentation into the interval [1,2] according to the followingformula: $x_{k} = {\frac{x_{k} - x_{\min}}{x_{\max} - x_{\min}} + 1}$conducting regression prediction on the compressor physical speed N_(c)and engine exhaust gas temperature EGT by using the aero-enginetransition state acceleration process test data after dimensionreconstruction, and calculating the response evaluating indicators;evaluating indicators comprise: (1) relative error RE formula of therelative error is:${{RE} = \frac{{\hat{y_{i}} - y_{i}}}{y_{i}}},{i = 1},{2\mspace{14mu}\ldots\mspace{14mu} N}$where, ŷ_(ι) is the predicted value of the sample at the i^(th) moment,y_(i) is the observed value of the sample at the i^(th) moment, and N isthe length of the sample; (2) Mean Square Error MSE mean square error isa measure reflecting the difference between the predicted sequence andthe observed sequence, and is calculated according to the followingformula:${MSE} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}( {y_{i} - \hat{y_{i}}} )^{2}}}$where, ŷ_(ι) is the predicted value of the sample at the i^(th) moment,y_(i) is the observed value of the sample at the i^(th) moment, and N isthe length of the sample.